Sauce: Preheat a heavy non-aluminum Dutch oven or similar 6-quart
pot over moderately high heat and add the olive oil. When the oil is
fragrant, add the chicken meat pieces and sauté, turning frequently
for 5 or minutes until lightly browned on all sides.

Add the onions and carrots and sauté, stirring constantly, until the
onions are translucent, about 2 minutes. Add the garlic and sauté
about 30 seconds. Do not allow the garlic to brown. Immediately add
the broth to the pot. Stir bits and pieces loose from the bottom of
the pot. Add all additional ingredients, lower the heat to a gently
simmer and cover the pot. Simmer gently, stirring occasionally,
until the chicken meat pieces are tender, but not soft, about 5 to
10 minutes.

As the sauce is finishing cooking, add 3 tablespoons oil to a heavy
skillet and sauté the bell peppers, squashes and broccoli over
medium heat until just crisp-tender. Add the veggies to the sauce
when the chicken meat is tender, blend all together and turn off the
heat. Adjust the salt, pepper and herb levels to taste. Toss the
cooked pasta with 1 tablespoon oil to prevent sticking and add to
the sauce; blend chicken, veggies and sauce thoroughly and serve
along with Parmesan cheese.